I According to my experience fresh new domain is very good for getting raniking soon in compare to old and affected by poor backlinks. So, start quality work from begning you can get good ranking in 2-3 months.

I dont think it is that tough to make new domain rank. In fact I have noticed that new website pages get crawled frequently. Plus you can start with the clean backlink profile while old domain age sites might have some spammy backlinks as they started getting backlinks when google was not so strict and any type of backlink would have worked at that time.